advancing drag crisis of a sphere

7/26/2019 Advancing Drag Crisis of a Sphere

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Wind and Structures, Vol. 14, No. 1 (2011) 35-53 35

Advancing drag crisis of a sphere via the manipulationof integral length scale

Niloofar Moradian1a, David S-K. Ting1band Shaohong Cheng*2c

1Department of Mechanical, Automotive and Materials Engineering, University of Windsor,

401 Sunset Avenue, Windsor, ON, Canada N9B 3P42Department of Civil and Environmental Engineering, University of Windsor,

401 Sunset Avenue, Windsor, ON, Canada N9B 3P4

(Received July 16, 2009, Accepted May 19, 2010)

Abstract. Spherical object in wind is a common scenario in daily life and engineering practice. Themain challenge in understanding the aerodynamics in turbulent wind lies in the multi-aspect of turbulence.This paper presents a wind tunnel study, which focuses on the role of turbulence integral length scale on the drag of a sphere. Particular turbulent flow conditions were achieved via the proper combination ofwind speed, orifice perforated plate, sphere diameter (D) and distance downstream from the plate. Thedrag was measured in turbulent flow with 2.2 104 Re 8 104, 0.043 /D 3.24, and turbulenceintensity Tu up to 6.3%. Our results confirmed the general trends of decreasing drag coefficient andcritical Reynolds number with increasing turbulence intensity. More interestingly, the unique role of therelative integral length scale has been revealed. Over the range of conditions studied, an integral length of

approximately 65% the sphere diameter is most effective in reducing the drag.Keywords: sphere; orifice perforated plate; turbulence; drag coefficient; integral length scale.

1. Introduction

Lowering the drag associated with a bluff body such as a sphere is of both fundamental and

practical importance. For example, when designing a golf ball, dimples are created on its surface to

lower the Reynolds number at which the drag crisis occurs, enabling it to travel a longer distance

compared to its smooth surface counterpart. It is now known that the standardized dimple design

has not been optimized to give the golf ball the best aerodynamic performance. This appears to be

partially due to the fact that wind turbulence has not been carefully considered in the classical

design. The omnipresent turbulence can significantly alter the aerodynamics of a sphere in an

otherwise laminar flow stream.

Extensive research efforts have been dedicated to understand the aerodynamics of a smooth sphere

in no turbulent (or smooth) flow conditions. Fig. 1 portrays a collection of experimental and

* Corresponding Author, Associate Professor, E-mail: [email protected] Graduate Studentb Professorc Associate Professor


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36 Niloofar Moradian, David S-K. Ting and Shaohong Cheng

numerical data from existing literatures (Shepherd and Lapple 1940, Torobin and Gauvin 1959, Clift

and Gauvin 1970, 1971, Achenbach 1972, Schlichting 1979), of which the relation between drag

coefficient CD and Reynolds number Re in smooth flow condition is shown by the shaded band.

This shall be referred to as the standard CDRe curve in the current paper. The flow pattern around

a sphere, particularly in the wake region, varies with the Reynolds number. For 10 3 < R e < 1 05,

which covers the Reynolds number range of 2.2 104to 8 104considered in the present study, the

vortex loop shedding becomes nearly a continuous process (Lamb 1945). Flow visualization (Bakicand Peric 2005) shows that the far wake region continues to grow in size and produces a wave-like

motion. Fig. 1 shows that the value of CDvirtually remains constant in this regime. As we approach

the critical Reynolds number, Recr 3.5 105, the boundary layer around the sphere transits from

laminar to turbulent, leading to the increased momentum near the boundary and the delay in flow

separation ( engel and Cimbala 2006). The wake region becomes narrower, resulting in a sudden

reduction in the drag coefficient (Schlichting 1955).

As most flows encountered in practice and in nature are turbulent flows, the influence of flow

turbulence on sphere aerodynamics has been the subject of numerous wind tunnel studies (e.g.,

Dryden and Kuethe 1930, Ahlborn 1931, Dryden et al. 1937, Brownlee 1960, Torobin and Gauvin

1960, Clamen and Gauvin 1969, Clift and Gauvin 1970, Anderson and Uhlherr 1977, Sankagiri and

Ruff 1997, Mohd-Yusof 1996). The consensus of these experimental studies is that an increase in

turbulence intensity would reduce the value of Reynolds number for boundary layer flow transition.

In other words, the value of the critical Reynolds number, Recr is very sensitive to free-stream

turbulence. This finding supports Prandtls (1914) suggestion that such resistance curves of sphere

can be used to compare the flow characteristics in different wind tunnels; in particular, with respect

to their lesser or greater turbulence. However, most of these past studies only focused on the effect

of turbulence intensity on sphere aerodynamics. For example, Dryden et al. (1937) pointed out that

for turbulent flow over a stationary sphere, turbulence intensity was the most important turbulent

parameter that affects the critical Reynolds number. The value of Recrwas decreased from 3.5105

in smooth flow condition to around 105 when the turbulence intensity was increased to 4.5%.

Torobin and Gauvin (1960, 1961) and subsequently, Clamen and Gauvin (1969) measured drag on

C

Fig. 1 Drag coefficient of sphere as a function of Reynolds number for different Tu


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Advancing drag crisis of a sphere via the manipulation of integral length scale 37

moving spherical bodies. A grid system was used to generate turbulence in the wind tunnel. Sphericalobjects of different sizes were injected upstream of the tunnel to have velocities close to that of the

oncoming air stream. It was found that the CD-Re curves corresponding to different turbulence

intensity levels had similar shapes except that the minimum-maximum CD occurred at different

Reynolds numbers. When increasing Re beyond Recr, the drag coefficient of their moving spheres

first increased and then decreased. They speculated that the increase in CD, right after its dip at Recr,

could be due to the occurrence of super turbulent flow regime. In more intense turbulent flow, the

magnitude of the maximum CD tended to be greater, whereas the corresponding Reynolds number

was smaller. In addition, Clift and Gauvin (1970) numerically studied stationary and moving

spherical particles in turbulent flow. By defining an equation to predict the value of critical Reynolds

number associated with flow of different turbulence intensities, it was shown that the critical

Reynolds number decreases with increasing turbulence intensity. Results from these studies are also

presented in Fig. 1. A more recent moving sphere drag measurement by Sankagiri and Ruff (1997) in

high turbulence intensity flow (Tu more than 30%) covered the sub-critical, critical, and super-critical

Reynolds number regions. In the sub-critical range, the drag was found to be greater than the

standard one with a gradual decrease into the critical regime. The behavior at the critical and super-

critical Reynolds numbers agreed fairly well with previous study by Clift and Gauvin (1971).

When studying aerodynamics of a bluff body in turbulent flow, it is important to appreciate the

complicated multi-aspect nature of turbulence; i.e., other than the turbulence intensity, the integral

length scale, which represents the size of the energy containing eddies, is yet another parameter of

great significance in defining the flow condition. A change in turbulence intensity typically leads to

associated variations in the turbulent length scale. Nevertheless, only a few researchers noted the

possible role played by the integral length scale when altering turbulence intensity in their studies.

Torobin and Gauvin (1961) varied the relative integral length scale /D (where D is the spherediameter) from 2 to 6.25 for 500 < Re < 2100, but failed to detect a definite role of /D in the CD-Re relationship. For lower Reynolds numbers, 200 < Re < 800, Zarin (1970) and Zarin and Nicholls

(1971) found that for turbulent wind over a fixed sphere, where the integral length scales were an

order of magnitude larger than the sphere diameter, the drag increased with increasing Tu from

0.4% to 3.3%. They also reported a monotonically decreasing CD with increasing sphere diameter

over 600 Re 5000, and 0.16 /D 2. Neve (1986) and Neve and Shansonga (1989) studiedsphere drag of a fixed 37.7 mm diameter sphere for 5103 < R e < 1 05, Tu < 25% and /D < 5.While no specific conclusion regarding the relative integral length effect was reached, their results

showed that at certain combination of turbulence intensity and relative integral length scale, the drag

coefficient could be reduced to less than 0.15; see Fig. 2.

It is clear from the literature review that there is a qualitative consensus concerning the effect of

turbulence intensity on the CDRe relationship of a sphere in turbulent flow. Quantitatively,

however, the discrepancies among different studies are overwhelming. The main factor contributing

to these discrepancies is probably , which has neither been measured nor controlled in moststudies. This integral length which is coupled with Tu, can significantly affect CD under some

conditions. Therefore, an attempt is made to assimilate the turbulent wind by quasi-independently

controlling the energy containing integral length scale, in addition to the turbulence intensity and

Reynolds number. Specifically, this study aims at uncovering the independent role of relative

integral length scale /D on the drag of a sphere when approaching the critical Reynolds numberrange. The preliminary results obtained by using three stationary PVC spheres in a wind tunnel over

a Reynolds number range from 2.2 104 to 8 104, turbulence intensity up to 10.7%, and relative


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integral length scale /D of 0.1 to 2.6, have been reported in Moradian et al. (2009).

2. Experimental details

2.1 Turbulence generation

The experiments were conducted in a low-speed, closed-loop wind tunnel at the University of

Windsor. The 4 m long test section is 0.75 m by 0.75 m at the inlet and expands to 0.765 m 0.765 m

at the outlet to accommodate boundary layer built up. The maximum attainable velocity of the wind

tunnel is around 20 m/s. The background turbulence level is found to be less than 0.3%.

Three 6 mm thick orifice perforated aluminum plates were used to simulate different turbulent

flow conditions. The turbulence was generated by placing one of the three plates near the inlet of

the wind tunnel. As sketched in Figs. 3(a) to 3(c), the hole diameter d of the plates were 25 mm,

37.5 mm and 50 mm, respectively. The solidity ratio of all three plates was kept the same at 43%.

To minimize the impact of the plate thickness on the generated turbulent flow field, each hole was

machined into an orifice with a 41oangle, as illustrated in Fig. 3(d). The same turbulence generation

mechanism was adopted by Liu and Ting (2007) and Liu et al. (2007), of which it was concluded

that an orifice perforated plate of 6 mm thickness, 41o orifice angle, and 43% solidity ratio was

appropriate for generating clean, simple, quasi-isotropic turbulence. The flow field was found to be

uniform in terms of mean flow velocity, turbulence intensity and integral length scale in the core

region of the testing cross section.

For quantifying flow velocities and the associated turbulent parameters, a hot-wire system

Fig. 2 The effect of relative integral length scale on drag coefficient: Tu = 10%, (/D) = 0.08, Neve (1986); Tu = 10%, (/D) = 0.5, Neve (1986), Neve and Shansonga(1989); Tu = 10%, (/D) = 0.8, Neve (1986), Neve and Shansonga (1989);Tu = 10%, (/D) = 1.5,Neve (1986), Neve and Shansonga (1989); Tu = 2.5%, (/D) = 0.63, Moradian et al. (2009); Tu= 4%, (/D) = 0.67, Moradian et al. (2009); Tu = 6.3%, (/D) = 0.7, Moradian et al. (2009)


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composed of a Dantec 55P61 X-type hot-wire probe with two Dantec Streamline 55C90 hot-wireanemometer (CTA) modules, a temperature probe, an A/D converter, a light-duty 2-D traversing

system and a computer, was used. The instantaneous flow velocity in the streamwise direction was

measured by the X-probe. The traverse system was secured at the desired locations downstream of

the orifice perforated plate along the wind tunnel center line for supporting the hot-wire probe and

the temperature probe. Previous study (Liu and Ting 2007) showed that the turbulence generated by

the orifice perforated plate remained non-isotropic until the wake-jet interactions mingled over a

distance of approximately 10d downstream of the plate, where d was the diameter of the holes of

the orifice perforated plate. Thus, all hot-wire data in the current study were collected at or beyond

10d downstream of the orifice perforated plate.

The measurement was taken over a period of 125 seconds at a sampling frequency of 80 kHz,

resulting in 10,000,000 samples at each measurement location. The sampling number was chosen

based on sensitivity analysis which would ensure stable and accurate mean velocity, turbulence

velocity and integral length scale deductions. The collected data were low-passed at 30 kHz to

avoid the aliasing problem before further analysis. A Pitot-static tube was employed at the

beginning of the tests when adjusting the wind tunnel power supply to provide the desirable wind

speed. It was removed during hot-wire and drag measurements.

2.2 Sphere setup

Six wood spheres with diameters D of 20, 51, 65, 102, 140 and 210 mm were used in the present

study to cover a Reynolds number range of 2.2 104 to 8 104, and to enable the independent

Fig. 3 The orifice perforated plate


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control of relative integral length scale /D varying from 0.043 to 3.24. The surface of all thespheres were polished and waxed. The surface roughness was measured by the Ra method inmaterial science (Czichos et al. 2006). The mean surface roughness was 17 m, giving a relative

roughness (surface roughness/sphere diameter) of no more than 8.5 10-4 for the smallest sphere

utilized. In other words, based on the mean surface roughness, the spheres were both mechanically

and hydraulically smooth.

To minimize the influence of sphere support on the results, 0.5 mm diameter high strength

polymer strings (SF24G-150 model of the FUSION brand) with a maximum tensile capacity of

10.9 kg were used to secure the sphere in position. Two holes of 5 mm in diameter and 20 mm in

depth (except for the smallest sphere, which had a depth of 9 mm) were threaded into the top and

bottom side of each sphere, allowing the fastening of the supporting strings via two screws. The

holes were filled with Epoxy once the screws were tightened.

A total of eight strings were utilized in the sphere setup, four of which were fastened to the top

hole and another four to the bottom one, as schematically illustrated in Fig. 4. The other end of the

top strings were laid symmetrically and fastened firmly to the two wind tunnel side walls with each

making an angle of [90o ( 0.3o)] with respect to the test section ceiling and 0.3o to thestreamwise direction of the wind tunnel. For the four bottom strings, their other ends were secured

firmly to the tunnel floor, making an angle of [90o (' 0.3o)] with respect to the test section floorand 0.3o to the streamwise direction of the wind tunnel. The string setup angles, which varied

depending on the sphere size, are listed in Table 1.

2.3 Drag measurement

To measure the drag force on a sphere, a load cell (model ELG-V-1N-L03M ENTRAN) wasemployed to quantify the net force in the strings. It was connected to a model MROJHHSG Electro-

Numerics amplifier which provided a 10 V excitation to the load cell. Due to the high strength of

the strings and the sphere supporting mechanisms designed for the current tests, vibration of sphere

induced by wind was minimal. When the sphere was subjected to wind, only the four upstream

strings, two at the top and two at the bottom, would resist the drag force on the sphere. In a typical

test with specified wind velocity and turbulence level, the load cell was attached to one of the top

upstream strings and one of the bottom upstream strings to quantify the net load within these two

strings. Due to the symmetric layout of the strings, the drag of the sphere was therefore deduced

from two times the sum of the horizontal streamwise components of the net loads in these two

strings. The following equations were used to calculate the drag force:

Streamwise net component in one top string

FD_Top = sincosFtop (1)

Streamwise net component in one bottom string

FD_Bottom = sin'cos'Fbottom (2)

Total drag force on the sphere

FD = 2(FD_Top+FD_Bottom) (3)


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In the present study, at each studied Reynolds number between 2.2 104 and 8 104, the proper

combination of orifice perforated plate hole diameter, sphere size and sphere location allowed the

Fig. 4 Schematic of the experimental setup


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quasi-independent variations of turbulence intensity and relative integral length scale from 2.5 to

6.3% and from 0.043 to 3.24, respectively.

3. Results and discussion

In this series of wind tunnel tests, the investigation on the independent effects of Reynolds

number Re, turbulence intensity Tu, and relative integral length scale /D on sphere drag waslimited by the three available orifice perforated plates, the range of freestream velocity that the wind

tunnel could provide, and the length of the test section over which the turbulence was nearly

isotropic and significant. However, efforts were made to identify appropriate combinations of orifice

perforated plate, the sphere location downstream of the plate and the wind tunnel speed, underwhich at least three data points could be obtained to isolate the impact of different turbulent flow

parameters on the drag. To compare with the no turbulence freestream flow scenario, measurements

were also taken in the absence of the orifice perforated plate, i.e., in smooth flow where the

freestream turbulence was less than 0.3%.

3.1 Turbulence parameters

Integral length scale and turbulence intensity are two important parameters for describing

turbulent flow. The magnitude of integral length scale is largely dependent on the size of the holes

of the orifice perforated plate and also on the spacing between adjacent holes. The approach

adopted in this study is based on the Taylors frozen turbulence hypothesis (Taylor 1938), where is defined as the product of the local time-averaged velocity and the time scale estimated from

the autocorrelation coefficients of the instantaneous turbulence fluctuation velocity u. According to

Batchelor (1967), this hypothesis is valid for turbulence intensity up to 15%. The maximum

turbulence intensity achieved in this study was less than 7% and thus, the integral scale estimation

is expected to be reliable. Relative turbulence intensity represents the turbulence level of flow. It is

defined as the ratio of the root-mean-square velocity urms with respect to the time-averaged flow

velocity at a specific location under consideration.

The quasi-isotropic turbulence downstream of Plate d-37.5 at 10.5 m/s has been detailed in Liu et

al. (2007). The turbulence generated by the orifice perforated plate was found to be homogeneous

over the cross section normal to the mean flow direction with Gaussian-like turbulence fluctuation.

U

U

Table 1 String angle in the sphere setupSphere type Diameter of sphere, D (mm) ' '

Wood sphere

20 53.6o 49.8o

37.2o 40.9o

51 54.9o 51.2o

65 55.4o 51.8o

102 57.0o 53.4o

140 58.7o 55.2o

210 62.0o 58.7o

PVC sphere[Moradian et al. 2009]

20, 51 and 102 40.4o 45.2o 63.5o 59.7o


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The isotropy of the turbulence field has been portrayed by a streamwise/lateral turbulence intensityratio of approximately 1.1. The turbulence kinetic energy decays in a power law manner as

(4)

with the exponent n of 1.012, implying a self-preserving state of the orifice perforated plate

turbulence. Here, X is the streamwise distance downstream of the plate, X0 is the virtual origin, M

is the mesh size, A is the decay power law coefficient and n is the decay power exponent (n = 1 for

completely self-preserving isotropic turbulence). The exponent n from the current experimental

work varies between 1.02 and 1.09, depending on the plate and freestream velocity. It agrees

favorably with that of Liu et al. (2007) and also with the analytical value derived by Speziale and

Bernard (1992).

u2

U2

------ AX

M-----

X0

M------

n

=

Fig. 5 Variation of integral length scale downstream of the perforated plate


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Fig. 5 portrays the variation of integral length scale along the centerline of the wind tunnel withthe normalized distance downstream of the plate. It is clear from this figure that the integral length

scale is larger at higher wind speed, over the range of wind speed from 3.4 m/s to 12.1 m/s

considered. Also, the integral length scale increases along the downstream direction. This

phenomenon is more obvious when the wind speed is higher. The main source of uncertainty in the

velocity measurement (the hot-wire measurement) came from its calibration. This includes the

uncertainty in the reference velocity, the uncertainty in voltage reading, and the uncertainty

associated with curve-fitting. The maximum uncertainties in and urms are estimated to be 1.2%

and 2%, respectively, while their average uncertainties are estimated to be 1.1% and 1.7%,

respectively. The maximum and average uncertainties of the integral length scale are estimated to be

approximately 4.2% and 3.6%, respectively.

Fig. 6 depicts the variation of the turbulence intensity downstream of the orifice perforated plate

at the five tested wind speeds. Results show the expected power law decay of turbulence with

U

Fig. 6 Variation of turbulence intensity downstream of the perforated plate


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distance downstream of the turbulence generator, as described by Eq. (4). In addition, the turbulenceintensity at any given location downstream of Plate d-37.5 and Plate d-50 is insensitive to changes

in freestream velocity; see Figs. 6(b) and 6(c). This invariance is not quite achieved when using

Plate d-25 (Fig. 6(a)), probably because the small holes resulted in some unstable jet-wake interactions

which continue relatively far downstream of the plate and thus, changes in these jet-wake intensity

lead to some variations in Tu. The maximum and average uncertainties of the turbulence intensity

are estimated to be approximately 2.4% and 2%. It is worth mentioning that the results in Figs. 5

and 6 are consistent with those obtained by Liu et al. (2007), where the same turbulence generation

system was employed.

3.2 CDRe relation under smooth flow condition

The background turbulence in the absence of orifice perforated plate was found to be less than

0.3%. This level is quite typical in low-speed wind tunnels and hence, the measured drag is

expected to be close to the standard curve in Fig. 1. Fig. 7 presents a comparison among the CD-Re

relation obtained in this study, that in our earlier study (Moradian et al. 2009) and the standard

curve. The band of the standard curve is based on data from Shepherd and Lapple (1940), Torobin

and Gauvin (1959), Clift and Gauvin (1970, 1971), Achenbach (1972) and Schlichting (1979). The

uncertainty in the drag measurement came from four different sources - the sphere diameter

measurement, the velocity measurement, the air density deduction, and the load cell measurement.

The maximum and average uncertainties of sphere diameter measurement are 4% and 1.8%,

respectively. The uncertainties in time-averaged velocity, sphere diameter and air density lead to

average and maximum uncertainties of 2.1% and 4.2%, respectively, in Re. The maximum

uncertainties in the drag coefficient of approximately 10.0% occurred when using the smallestsphere at the lowest tested velocity; the typical uncertainties are around 7.8%. Fig. 7 shows that the

values of drag coefficient obtained in the current study fall within the band of the standard curve. A

Fig. 7 Drag coefficient versus Reynolds number in smooth flow


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small discrepancy between the current set of data and those by Moradian et al. (2009) can beobserved at lower Reynolds numbers. This is probably caused by the difference in surface

roughness. The smoother PVC spheres used in Moradian et al. (2009) have a mean roughness of

0.97; that is, less than 6% of that associated with the wood spheres used in this study. While all

spheres considered in this and our previous studies can be considered hydraulically smooth

(Moradian 2008), the smallest wood sphere used which gives the lowest Re data has the largest

relative roughness. It is possible that some part of the surface of this smallest wood sphere could

have slightly exceeded the roughness threshold which defines the sphere to be smooth.

3.3 CDRe relation in turbulent flow

It is known that the drag coefficient of a sphere undergoes a sudden drop at the critical Reynolds

number which is approximately 3.5105 under negligible turbulence condition. However, this value

can be significantly altered in the presence of turbulence. To explore the impact of different

turbulence parameters on the sphere drag and to identify the corresponding critical Reynolds

number, drag measurement was conducted on six wood spheres for 2.2 104 Re 8 104, Tu up

to 6.3%, and 0.043 /D 3.24. The variation of CD with respect to Reynolds number underdifferent turbulent flow conditions are plotted in Figs. 8 and 9.

The three subplots in Fig. 8 describe the CD-Re relation at turbulence level of 2.5%, 4% and

6.3%, respectively. Every curve in each figure corresponds to a certain relative integral length scale.

The general trend of decreasing CDwith increasing Re is obvious. The detail CD-Re pattern, on the

other hand, highly depends on the turbulence level and the relative size of the eddying motion

(integral length).

By comparing Figs. 8(a), 8(b) and 8(c), it can be concluded that at any particular Re and /D, thedrag coefficient CD is smaller in higher turbulent wind. This is more obvious at higher Reynolds

number. Also shown in Fig. 8 are the data from the three PVC spheres obtained by Moradian et al.

(2009); these results are in excellent agreement with the current set of results based on six wood

spheres.

When taking a closer look at Figs. 8(a), 8(b) and 8(c), it can be seen that among the turbulence

conditions (Tu = 2.5%, 4%, 6.3%) considered here, CDconsistently reaches its minimum when /Dis around 0.65. In other words, the value of CDdecreases with increasing /D up to 0.65, and thenit starts to increase with further increase in /D beyond 0.65; the values of CD at /D of 1.2 areapproximately equal to those at /D of 0.33. In short, for the range of relative integral length scaleinvestigated in this study, an eddy/sphere size ratio of approximately 0.65 appears to be most

effective for lowering CD.

Furthermore, it is observed from Fig. 8 that for Reynolds numbers less than 3.7 104, CD is

relatively insensitive to changes in eddy size and turbulence intensity. The influences of the relative

integral length scale and turbulence intensity become progressively more pronounced at higher

Reynolds numbers. Also, the drag coefficient is most sensitive to relative integral length scale at

high Tu when /D is around 0.65. For example, for the Tu 6.3% and Re = 8 104case shown inFig. 8(c), when the relative integral length scale is increased from 0.22 to 0.65, the drag coefficient

decreases by more than 55%, from 0.225 to 0.1; whereas when /D increases from 0.65 to 1.2, CDjumps up by 50%, from 0.1 to 0.15.

The data presented in Fig. 8 are reorganized in Fig. 9, to better reflect the effect of turbulence

intensity on sphere drag. Each subplot in Fig. 9 shows the CDRe relation at a particular relative


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integral length scale, and every curve in the figure corresponds to a certain turbulence level. In

general, for all the three turbulence intensity levels studied, the drag coefficient is observed to

decrease with increasing Reynolds number, for any /D condition. More importantly, the /D=0.65

Fig. 8 Variation of CDwith Re at constant turbulence intensity


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condition always leads to the lowest CDfor the same turbulence level, at any Reynolds number.

The general results of decreasing CDwith increasing Tu presented in Fig. 9 are in good agreement

with those in the literature (for example, Dryden et al. 1937, Torobin and Gauvin 1959, Clift and

Gauvin 1970), which suggest that the increase of turbulence intensity tends to advance the critical

Reynolds number as a result of movement of the separation point farther downstream of the sphere.

If we follow Torobin and Gauvin (1959) and define Recras the Reynolds number at which the value

of CDis less than or equal to 0.1, then this critical condition has not been reached under most of the

conditions plotted in Fig. 9. Nonetheless, the CDcorresponding to the higher turbulence level cases

all tend toward this critical value. The /D = 0.65 case at Tu = 6.3% in Fig. 9(c) indicates that this

Fig. 9 Variation of CDwith Re at constant relative integral length scale


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critical condition has been achieved at Re = 8 104

, which is significantly lower than the standardsmooth flow Recrof 3.510

5.

Looking closer at the results documented in the literature (Figs. 1 and 2), it is found that under

similar turbulent flow conditions, the critical Reynolds number values identified by Dryden et al.

(1937), Clift and Gauvin (1970) and Moradian et al. (2009) agree well with that obtained in this

study. As can be observed from Fig. 1, Dryden et al. (1937) found from their drag measurement of

a fixed sphere that at turbulence intensity of 4.5%, Recr was around 9104; whereas the numerical

simulation by Clift and Gauvin (1970) showed a critical Reynolds number of 7 104 at Tu of 5%.

Moradian et al. (2009) conducted drag measurement on three PVC spheres in turbulent wind, and

reported that at Tu = 6.3%, Recr was 8 104. The small discrepancy in the quantitative results is

believed to be not only induced by the slight difference in the turbulence intensity, but also some

variation in /D.

3.4 Combined effect of turbulence parameters on CD

As pointed out earlier, turbulent flow has a complicated multi-aspect nature, of which the flow

parameters such as turbulence intensity and integral length scale are dependent on each other. To

better grasp how sphere drag would be affected by the presence of turbulence in the oncoming flow,

the CDRe relation is shown three-dimensionally in Fig. 10. The surfaces are contours of particular

turbulence intensity. The fact that CD is lowered with increasing Tu can be readily observed. The

effectiveness of this reduction is enhanced at higher Reynolds number. More interestingly, all CDcontours dip at /D 0.65, where the minimum CDoccurs.

Fig. 11 shows the results achieved by Neve (1986), Neve and Shansonga (1989) and the

comparison between them and current results. As shown in Fig. 11(a), for their fixed sphere inturbulent freestream with Tu = 10% the effect of /D is inconclusive. Even though freestreamturbulence with /D of 1.5 seems to significantly lower the drag coefficient for Re < 2 104, this/D effect diminishes at higher Re. At a higher Tu of 16% (Fig. 11(b)), on the other hand, a

Fig. 10 Variation of drag coefficient with Re, Tu and /D


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smaller integral length /D of approximately 0.75 leads to appreciably lower CD, and thatfreestream turbulence with /D of 3.5 results in relatively larger CD for Re > 1.2 104. In short,Neve and Shansonga did not reach any definite conclusion regarding the role of /D. The resultsobtained in this study (see Fig. 11(c)), on the other hand, portray a clear trend of reduced CDat /Dof about 0.65.

Physically, an increase in flow turbulence advances the boundary layer transition into a turbulent

boundary at a lower Reynolds number compared to its smooth flow counterpart. This reduces the

Fig. 11 A comparison CD= f(Re, Tu and /D)


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unfavorable pressure gradient around the sphere and hence, moves the separation point fartherdownstream. Consequently, the pressure drag is progressively lowered with increasing freestream

turbulence. The underlying physics played by the (relative) integral length is less known. Intuitively,

there are probably two key dimensions associated with a flow over a sphere. One of these is the

thickness of the boundary layer, especially that just upstream of the separation point. The larger

dimension is defined by the size of the wake, which can be approximated by the diameter of sphere.

The results obtained in this study seem to suggest that, over the range of conditions considered here,

turbulent flow with eddy sizes falling in between the small dimension of the boundary layer and the

large dimension defined by the wake is most effective in advancing the drag crisis. In other words,

an integral length of about 65% the diameter of the sphere appears to be most effective in perturbing

the boundary layer from laminar to turbulent, and in decreasing the size of the (near) wake.

Nonetheless, it is possible for the optimum value of /D, which corresponds to the lowest CD, todeviate from 0.65 at other (higher) turbulence conditions. It is also plausible to have more than one

CDminimum, especially at very high turbulence levels. While not achieved in this study, the results

obtained by researchers such as Torobin and Gauvin (1960) as shown in Fig. 1 appears to indicate

the possibility to have a sunken saddle prior to the occurrence of the advanced drag crisis at higher

Re. If this is truly the case, it is likely that the corresponding optimal /D values for the sunkensaddle and that associated with the advanced drag crisis are different.

4. Conclusions

This paper presents an experimental study on advancing the drag crisis of a sphere via the

manipulation of turbulent integral scale. Six wood spheres were tested in a closed-loop wind tunnelfor 2.2 104 Re 8 104. Turbulence was generated by orifice perforated plates with turbulence

intensity up to 6.3% and relative integral length scale /D from 0.043 to 3.24. The variations ofsphere drag with respect to Reynolds number under different turbulence conditions, were obtained

and compared with that in negligible turbulence condition. It has been confirmed that the drag

coefficient can be decreased and the critical Reynolds number can be advanced by increasing the

flow stream turbulence intensity. More interestingly, the unique role of the relative integral length

scale has been revealed. At any studied Reynolds number, the optimum size of integral length scale

on lowering drag with increasing Tu is found to be about 65% the sphere diameter. In other words,

decreasing /D down to 0.65 increases the effect of Tu on reducing drag, while reducing /D below0.65 would lessen the influence of Tu.

Acknowledgments

The project was made possible through the financial support from Natural Sciences and

Engineering Research Council of Canada (NSERC).

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CC

Nomenclature

A decay power coefficient

CD drag coefficient

D diameter of spheres (m)

d diameter of holes of the orifice perforated plates (m)

Fbottom net force in a bottom string (N)

FD_Bottom streamwise net component in a bottom string (N)

FD_Top streamwise net component in a top string (N)

Ftop net force in a top string (N)

M mesh sizeN sampling number

n decay power exponent

Re Reynolds number, UD/Recr critical Reynolds number

Tu turbulence intensity, urms/ (%)

U mean flow velocity (m/s)

time-averaged velocity (m/s)

u instantaneous fluctuating velocity (m/s)

urms root mean square velocity (m/s)

X streamwise distance downstream of the plate

Xo

virtual origin

Greek Symbols

integral length scale (m), ', , ' angles associated with sphere attachment with respect to the walls (deg)

U

U

advancing drag crisis of a sphere

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